Left hand isnt deforming even though its properly weight painted?
It's not properly weight painted:



As you can see thoose are the vertices which doesn't move as expected; in the "N" panel, vertex weight tab, you can read their assignements: HandL and ArmR.

You can use the vertex group tab to remove unwanted weight (armR) and apply some weight on the desired vertex group (maybe armL.003). 

In the armature modifier enable theese little two buttons to see the poses also during edit mode.

If you used some automatic weight assignement and automatic flip names, the problem came because all names should END with .L or .R (not armL.003); .l and .r are OK too, but always on the end of the name.